Slide rule with logarithmical graduations



Dec. 4, 1923., 7 1,475,999

P. JARAY SLIDE RULE WITH LOGARITHMICAL GRADUATIONS Filed {June 28 1920 2 Sheets-Sheet 1 INVENTORI j /L m Dec. 4 1923. 1,475,999

P. JARAY SLIDE RULE WITH LOGARITHMICAL GRADUATIONS Filed June 28 1920 2 Sheets-Sheet 2 [I J v 9 7616' 1 a J? F 1 & W 4 J Patented Dec. 4, 1923.

UNITED STATES PATENT OFFICE.

PAUL JABAY, 0]! FRIEDRICHSHAFEN, GERMANY, ASSIGNOR TO THE FIRM LUFT- SCHIFFBAU ZEPPLIN GESELLSCHAFT MIT BESCHRANKTER HAFTUNG, OF FRIED- nrcasnarnn, GERMANY.

SLIDE RULE WITH LOGARITHMIGAL GRADUATIONS.

Application filed June 28, 1920. Serial No. 392,570.

T 0 all whom it may concern:

Be it known that I, PAUL J ARAY, a citizen of the Austrian Republic, residing at ,Friedrichshafen, Germany, have invented certain new and useful Improvements in Slide Rules with Logarithmical Graduations, of which the following is a specification.

My invention refers to slide rules with logarithmical 'graduations and concerns substantially the arrangement and develop-- ment of the scales. By means of rules of this kind given figures can be directly multiplied together and divided, -i. e. expressions like c bxc etc., can be verified at once. But when the definite figure is replaced by an algebraic sum of the form (uXoi-w) or each other by an assemblage of connecting lines in such a manner that corresponding points of both scales invariably show the same numerical difference. If such a slide rule is designed for general calculation rather than for the solution of certain special problems, in which the figures u, v and w of the algebraic sum are variable to a certain extent only, it can be improved further by a certain modification of the individual scales. -By doing this according to its special development new fields of application are opened, in which a quick verification of the results of numerous values observed is very valuable or rather necessary, but could not be effected without any special intermediate calculation or a sometimes confusing use of auxiliary tables.

An important special problem of this kind, whose quick and complete solution by means of a slide rule could not be efiected heretofore, was the calculation of the lifting power of air-balloons. The total lifting power of an air-balloon or of an airship is known not to be a definite value, but it depends, apart from the properties of the gas, upon many outer influences often changing quickly during a and temperature, the balloon.

V may signify the volume of the balloo fully inflated.

o the height of the barometer.

and upon the inflation of voyage, such as pressure T (273+t the temperature of the gas at the greatest height the balloon had reached u to the moment of the verification o the lifting power. T (273+t the temperature of the gas at the moment of the verification of the lifting power. T (273+t the'temperature of the air.

d the proportion of the gas density to air density at equal power and tempera ture.

1 a figure of correction which depends upon the degree of humidity of the air and differs from zero, if at all, only at higher temperatures.

K constant and V A the required resulting lifting power of the balloon; then this equation witl express the conditions:

' wherein 4 may be neglected with close and fit) for most practical measurementsamply sufficient approximation and wherein a? can be taken for a constant. Under this assumption the whole lifting power is:

The desired value A thus depends upon seven other values, five of which, namely the expressions V, M, T T T are variable. The variability does not extend over the whole range of figures, but is limited by certain upper and lower limits according to their scientific signification. To utilize this limitation of the individual figure ranges to attain a special clearness and easy handling of the slide rule is a further aim of the invention.

According tothe present invention this aim is attained by a slide rule fitted with some moving slides, in which the scales connected by the time connecting line are preferably longitudinally staggered relatively to each other, but in which each scale shows only one kind of concrete numbers and comprises only the range of figures valid for these numbers according to their physical meaning. As a further extension of the invention referabl for the movin scalesof those numbers, which according to their scientific signification possess parametric quality, i. e. represent for some time a value substantially invariable, Special arresting appliances are provided.

Tn the drawings affixed to this specification and forming part thereof several modifications of the object of the present invention are illustrated by way of example in as to graduation and arrangement.

various positions of the slide.

In the drawings Figs. 1 to 5 show a slide rule designed mainly for general calculations fitted with one moving slide, and

Figs. 6 to 9 a slide rule fitted with several slides and designed especially ,for the calculation of the lifting power of airships.

The slide rule according to the first modification consists of a body A and a moving slide B. The slide possesses a bottom scale 79 and a top scale I) of the ordinary logarithmical graduation.

The body has corresponding scales a and a which-as on the ordinary slide rules correspond exactly to the coordinate figures of the slides and comprise as usually one or two decades. Moreover the body of the rule A contains in its upper part a scale a which is absolutely uniform with seal; (1';

- scales (1 and (1 are coordinated by an assemblage of connecting lines in such a manner that each point of the .lower line a corresponds to the same point minus one unit of the upper scalea By me'ans of the slide rule allknown operations Such as multiplying, dividing etc. can be executed. Moreover expressions of the form (uxv'iw) and may be determined at" once and multiplied and divided by other figures. In the simplest case u, 'v and w represent known quantities, but they may be as well products or quotients of such. In order to utilize the object of the invention for the verification of the algebraic expressions given above they should be imagined as being written in this form:

a 'u X1) 1 1 w and x to i l w. Two simple numeric examples may 'serve as illustrations.

1. The value e x 1.5 2=(g 1.5%)2

is to be determined.

The slide B (Fig. 2) is shifted to the right until 2 in scale 6 is below 6 in scale a The figure 1.5 of scale 6 then coincides with figure-4.5 of scale of. The correspond ing connection line 0 leads to figure 3.5 in

gure 6 in scale a, which may be marked by the window slide. If then slide B (Fig. 5) is shifted until its figure 2 appears in the window, i. e. coincides with figure 6 a of scale M, the beginnin of the slide scale indicates the .desired'resu t 3 in scale a. As both examples show, by twice or three times shifting the slide an algebraiesum of the tyII Je mentioned can be worked out.

. ven in this arrangement the slide rule can. be used for lifting ower calculation according to equation 2-,

The connecting line a belonging to a" leads to ut a certain dis rule for lifting power calculation, as shown by the second modification, of which Fig. 6 gives a general View and Figs. 7 to 9 partial views on a larger scale. I

The slide rule has three stationary guide bars A, A and A" and three moving slides B, C and D. The slides B and C glide in direct touch with one another between the upper and the middle guide bar. The slide D glides between the middle and the lower spaced relatively unit,

guide bar. The upper guide bar A has a marka The upper slide B has an upper scale 1) giving the gas bag volume in cubic metres and a lower scale b showing the temperature t from to +40". The middle slide contains an. upper scale 0" and a lower one 0. The former indicates the barometric pressure 6 in millimeters of mercury, extending from 350 mm. (corresponding to an absolute height of ca. 6000 m.) to 800 mm. (very high barometric pressure at sea level). On the lower scale 0 the resulting lifting power A is given in kilograms. The middle guiding bar the left two upper scales a and w to which are coordinated two lower scales (1 and (1 by means of two assemblages of connecting lines F and E. Moreover on the middle guide bar a scale a is provided for the temperature t extending from 40 to +40-.

The bottom slide D has on the left two scales 9 and d for the proportion of gas density to air density. Further to the right is a scale al for the temperature 6 extending from 40 to +40, whose figures for the sake of greater accuracy are corrected by the correcting factor (-1- 4) allowing for the humidity of the air. Besides a window slide F is provided. By set-screws and H inserted in the back of the slide rule body the slides B and C can be locked.

The scales b b 0, 0", a and af' show an identical logarithmic graduation. Equally the scales a, a, a (1, d and ai are fitted with a logarithmic graduation of the same In order to facilitate the handling of the device of the slide rule several scales e. g. (H, a and a as well as d, d and d are to each other by certain distances equal for the corresponding pairs. The diagonal or connecting lines E and E connect coordinatequantities whose figure values differ by the average proportion of gas density to air density. With illuminating gas this proportion varies from 0.36 to 0.44 and is at an average 0.40; with hydrogen the value varies from 0.07 to 0.13;

y with reference to the two scales a and a A has on in scale a of slide the average is 0.10. Accordingly each point of the illuminating gas scale a is increased by 0.4 units as compared to the coordinate point of scale a; equally each point of scale a is smaller by 0.10 units than the coordinate point of the hydrogen scale (1 in a similar manner, as hereinbefore described In both cases the division point of one of the coordinate scalesis connected by a diagonal line or the like to the division point of the opposite scale which corresponds to the division point first referred to including a positive or negative increment.

The handling of the slide rule will be illustrated by some examples in figures. The general constant has in round figures the value K:0.45. To determine the resulting lifting power A of a free balloon of 7:600 cbm capacity, which at sea level (6 :7 mm. of Hg.) and at a temperature Q: 22,: t z0 is fully inflated and which is filled with heavy illuminating gas of a density d:0.44.

Slide B (Figs. 7 and 8) is shifted until figure 6 in scale 72 coincides with the mark a and is locked in this position by set-screw G. Then slide C is shifted so that the figure b =760in scale 0* coincides with 13;:0 in scale 6 Slide D is left in its normal position (Figs. 6 and 7 as in this the values Z O and t :0 in the scales (t -and 05 coincide normally. Then division (1:044 in scale d on top coincides with a division of scale a. If now the window slide is set u on the corresponding division of scale a, t "e figure 4.21 is read in scale 0 of slide C. The desired result, i. e. the lifting power is thus A'=421 kg.

Assume-that when the balloon without throwing oif ballast has reached a height of about 900 metres (corresponding to a barometric pressure b :680 mm.) at a gas temperature t :5 C, it reaches warmer currents of air and starts sinkin whereby the gas is again somewhat warmed. Shortly before the landin thetemperature of the air may be assume to be .t .+10 and the gas has been warmed to m: +5 G. How much ballast must be thrown off during the sinking to just keep the balloon in equilibrium? Slide C (Fig. 9) is shifted so that the figure 12 680 in scale 0" comes below figure t -5 of the set scale I) (and set-screw H is referably tightened). Now slide "1) is shi ted so that t :-}1O in scale (1 coincides with figure t :+5 in scale a The division (1:044 in scale d thus coincides exactly with a division of scale a. If the window slide is shiftedupon the coordinate division of scale a, it covers the figure 3.70 C. This means that the existing lifting power is still A:370 kg, i. e. it has been reduced compared to the start of the voyage by 421370=51 kg.

ill

The ballast thrown ollmuet at least anal this weight, lit more hallaat is throw that the balloon rises again, theslides .o and C may be left clamped for the further voyage provided that the original hi hest altitude otSOO mm. (h zddll e not exceeded. Thus the lifting power can he a?- certained at any moment in a most simple manner by bringing to coincidence the measured temperatures of air and gas #1, and t by means of the bottom slide and covering by the window slide the upper end of connecting line lE corresponding to scale vision dzO/l t. in scale a the resulting lilting power can thus always be read ofi. As each scale has one meaning and comprises the necessary ranges of figures only, error and waste of time in handling are minimized.

its all scales are free for inspection at the same time, all proportions can be ascertained at a glance, no matter which of the numerous figures is wanted.

lln exactly the same way the slide rule can be used if hydrogen is used for lifting. ut in this case the scales at, a and al 'are re.- placed by the scales a, a" and d As may be seen from Figs. 8 and 9 with a filling of hydrogen gas of 13:02.10 density the lifting power under otherwise equal conditions would be at the start 677 and near the sums occur as parts of products or quotients,

the slide rule could even he ll claim: 7 "1. In aslide rule the combination with a more simplified.

relatively stationary-graduated ruler, and

twoadjacent parallel sliding rulers, longitudinally displaceably mounted on such stationary ruler, of oppositely and alternately arranged equally numerically subdivided scale sections indicating respectively proportions of gas density and air density, and

volume indicating logarithmic scales on the other. sliding ruler 2. lln a slide rule the combination with a relatively stationary graduated ruler andtwo adjacent parallel sliding rulers longi tudinally displaceable on such stationary ruler, of oppositely and alternatingly arranged, equally numerically subdivided scale sections on 'suchstationary ruler, indicating respectively proportions of gas density and air density, and connecting lines'between the corresponding oppositely situated values for these density proportions, pressure indicating logarithmic graduations, and lifting power indicating graduations on one of said sliding rulers, and volume and temperature indicating graduations on the other sliding ruler, an additional sliding ruler on said I'stationary ruler and parallelly spaced from the first-mentioned sliding rulers, and containing a temperature scale and registerable with the scale sections of the station ary ruler, and a rider index movable along the stationary and movable slides.

3. ln a device of the kind described in combination, a rule, a plurality of slides movable relatively to said rule and of logarithmically graduated scales, on" slide carrying scales-for temperature and volume of t e gas, respectively, another scales for the height'ot the-barometer andfor the lifting power of gas respectively, athird scales for the temperature of the air and for the specific weight of the gas, respectively, and a mark, a scale for the temperature of the gas and a plurality of lines on said rule, said lines connecting the scales for the specific weight and for the lifting power of the gas in such wise that corresponding points of said scales present like numerical differences.

ln testimony whereof afiix my signature.

PAUL JARAY. 

